A person familiar with the transition efforts said different factions in Trump's team "are fighting for power"

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Hidden from the public in his Manhattan high-rise, Donald Trump huddled most of Tuesday with Vice President-elect Mike Pence as he tried to fill out key posts in his Cabinet. But the transition team appeared to be straining under the enormous challenge of setting up a new administration.

Former Rep. Mike Rogers, a respected Republican voice on national security issues, announced he was quitting the transition effort. And an apparent clerical oversight effectively halted the Trump team's ability to coordinate with President Barack Obama's White House.

With Trump out of sight for several days, his allies engaged in an unusual round of public speculation about his potential appointments — including their own futures — as the president-elect and his aides weighed the nation's top national security posts.

Former New York Mayor Rudy Giuliani seemed to be angling for secretary of state. But Trump's transition team was reviewing Giuliani's paid consulting work for foreign governments, which could delay a nomination or bump Giuliani to a different position, according to a person briefed on the matter but not authorized to speak publicly about the matter.

Giuliani founded his own firm, Giuliani Partners, in 2001, and helped businesses on behalf of foreign governments, including Qatar, Saudi Arabia and Venezuela. He also advised TransCanada, which sought to build the controversial Keystone XL pipeline, and helped the maker of the painkiller drug OxyContin settle a dispute with the Drug Enforcement Administration.

A Trump official said John Bolton, a former U.S. ambassador to the United Nations, remained in contention for secretary of state. Bolton has years of foreign policy experience, but he has raised eyebrows with some of his hawkish stances, including a 2015 New York Times op-ed in which he advocated bombing Iran to halt the country's nuclear program.

Businessman Carl Icahn disclosed on Twitter, based on conversations with the president-elect, that Trump was considering Steve Mnuchin, a former Goldman Sachs banker, and Wilbur Ross, a billionaire investor, to lead the Treasury and Commerce departments.

Pence, now running the transition team, ignored questions from reporters as he walked through the lobby of Trump Tower, a thick binder tucked under his arm. He took over from New Jersey Gov. Chris Christie, who spent months running transition operations before his demotion last week.

The switch has slowed Trump's ability to coordinate with the White House. Pence delivered a signed memorandum of understanding (MOU) to facilitate interactions between his team and Obama administration officials, a White House spokesperson confirmed Tuesday night. But there is more paperwork required from Trump's team before the White House can begin briefing incoming staff.

Indeed, Trump effectively created two power centers in his White House even before taking office. He named Republican National Committee Chairman Reince Priebus as his chief of staff and flame-throwing media mogul Steve Bannon as his chief strategist, but called them "equal partners." Trump's son-in-law Jared Kushner is also deeply involved in the transition, creating another layer of uncertainty about who is making decisions.

"That organization right now is not designed to work," according to the person close to the efforts, who like others involved in the transition, insisted on anonymity because they were not authorized to publicly discuss the internal process.

Former GOP national security official Eliot Cohen blasted Trump's team on Twitter, calling them "angry, arrogant." Cohen opposed Trump during the campaign, but in recent days, he said those who feel duty-bound to work in a Trump administration should do so. But he said Tuesday that after an exchange with Trump's team, he had "changed my recommendation."

With Trump's team divided, emboldened Republicans on Capitol Hill moved forward with a united front. House Speaker Paul Ryan, a lukewarm Trump supporter during the campaign, unanimously won his GOP colleagues' votes for another term at the helm of the House. He told fellow Republicans he had Trump's support, and heralded "the dawn of a new, unified Republican government."

"If Trump is serious about seeking unity, the first thing he should do is rescind his appointment of Steve Bannon," Senate Minority Leader Harry Reid said. "As long as a champion of racial division is a step away from the Oval Office, it would be impossible to take Trump's efforts to heal the nation seriously."

Trump's team has defended Bannon and tried to put its focus on filling the top national security jobs. Trump's selections will be the first signals to anxious international allies about the direction he plans to take U.S. foreign policy.

Alabama Sen. Jeff Sessions, a loyal Trump ally and immigration hard-liner, is said to be a contender for defense secretary.

Trump also is considering Richard Grenell as U.S. ambassador to the United Nations, which would bring some experience and diversity to his nascent administration. Grenell, who served as U.S. spokesman at the U.N. under President George W. Bush, would be the first openly gay person to fill a Cabinet-level foreign policy post.